Appreciate actually the overall take (although not sure how many would not have found most of it simply common sense anyway), but: A bit more caution with the stats would have been great

• Just-about-significant $\ne$ 'insignificant and basta'. While you say the paper shows up to incl. 27 there's no 'effect' (and concluding on causality is anyway problematic here, see below), all data provided in the graph you show and in the table of the paper suggest BMI 27 has a significant or nearly significant (on 95%..) association with death even in this study. You may instead want to say the factor is not huge (or small compared to much larger BMI variations), although the all-cause point-estimate mortality factor of roughly 1.06 for already that BMI is arguably not trivial at all: give me something that, as central-albeit-imprecise estimate, increases my all-cause mortality by 6%, and I hope you'd accept if I politely refused, explaining you propose something that seems quite harmful, maybe even in those outcomes where I don't exactly die from it.
• Non-significance $\ne$ No-Effect. Even abstracting from the fact that the BMI 27 data is actually significant or just about so: "not significant" reduction in deaths on BMI 18-27 in the study wouldn't mean as you claim "will not extend your life". It means, the study was too imprecise to be exactly 95% or more sure that there's a relationship. Without strong prior to the contrary, the point estimate, or even any value to the upper CI bound, cannot be excluded at all as describing the 'real' relationship.
• Stats lesson 0: Association $\ne$ Causality. The paper seems to purposely talk about association, mentioning some major potential issues with interfering unobserved factors already in the Abstract, and there are certainly a ton of confounding factors that may well bias the results (it would seem rather unnatural to expect people who work towards having a supposedly-healthy BMI to behave not differently on average in any other health-releveant way than people who may be working less towards such BMI).